The control of humanoid robots currently utilizes inverted pendulum model (IPM) to generate the center of gravity (CoG) dynamics, then uses Zero Moment Point (ZMP) to ensure the stability of motion. The limitation of IPM-based solution is that the support point of inverted pendulum is moving in the real motion, which leads to the error of the planned CoG trajectory. In addition, ZMP requires the information about the external force or torque to calculate the position of support point. Therefore, ZMP is unavailable for moving on the slippery ground. This research proposed a control method based on only the center of gravity information. The system can adjust the several input data to achieve the balance. A description of motion task is presented to transform a real motion task to a CoG trajectory and certain constraints. To plan a practical CoG trajectory, an close-form S - curve planning solution is proposed, which can be utilized online due to the time-efficiency. In the planning algorithm, the complicated logic decision is transformed into a quartic equation. A CoG controller is proposed and implemented to perform a desired task. To verify those algorithms and control methods, a platform for two-leg robot is established. The results of simulation and experiment show the effectiveness of the algorithm and the controller.

Singularity is a crucial problem for the inverse of a link chain in articulated robots, which can cause inverse algorithm fail and non-executable inversed joint velocities. The inverse in the velocity domain, so-called change rate method, is common-used inverse method but still involved in the dilemma. For the general singularity models, this paper proposed a solution in which the three variables of change rate method, joint velocities, Jacobian matrix and velocities in the Cartesian space, is systematically considered to eliminate the influence of singularity. The solution can theoretically achieve zero error caused by singularity. The executable feature of the solution is ensured by eliminating the singularity elements in the Jacobian matrix and introducing the limits of joint velocity in the planning algorithm. The key three issues is solved:​ separation of singularity elements, cancellation the singular terms in the separated elements, and planning required trajectories. The simulations verified the effectiveness of the proposed solution.

This research proposes a reachability-based controller to improve the performance of dynamic torque tracking for electromagnetic actuators. The principle and design process of the proposed controller are presented. To demonstrate the design process, a reachability-based controller is designed. Compared to most existing controllers that feed the system with a constant control output during a control period, the proposed controller outputs a series of points from the discretization of a continuous trajectory. Meanwhile, the error bound is estimated and its condition is derived. The experimental results show that the proposed controller is effective and robust. The smaller dynamic torque tracking error, less energy consumption and robustness against disturbances are achieved when compared to the PID controller.

This research systematically provides a solution to control humanoid robot only based on the CoG, avoids the limitation of the existing IPM-based solutions. The control method also provides the probability of online learning duo to the parameterized motion task planning. The solution to the singularity problem in the inverse kinematics can enable the establishing of the high precision control system. The controller for electromagnetic actuators can potentially improve the response speed of the devices in the industrial field.